"The research has shown that diet definitely affects some children. ... and some non-food items are relevant. Symptoms which may change include those seen in attention deficit disorder (ADD) and attention deficit hyperactivity disorder (ADHD), sleep problems and physical symptoms, with later research emphasizing particularly changes in mood."

Twelve children, aged six to 13 years, whose parents reported an improvement in behavioural problems with use of the
Feingold (K-P) diet for an average period of 12 months, were challenge-tested with 40 mg of acetylsalicylic acid in a
double-blind, cross-over trial with ascorbic acid as a placebo. ...
significance was reached in tests of general cognitive capacity, line walking and the "finger-to-nose" tests, as well as
increased disturbance in sleep patterns in these children.

"OBJECTIVE: Individuals with ADHD often report sleep problems. Though most studies on ADHD and sleep examined children or nonclinically diagnosed adults, the present study specifically examines nonmedicated adults with ADHD to determine whether inattentive and hyperactive-impulsive symptoms are associated with sleep problems.
...

CONCLUSION: The results show that sleep problems are associated with hyperactive and impulsive symptoms in nonmedicated adults with ADHD. These findings provide information on the nature of sleep problems without the confounding effects of medication associated with ADHD. Treatment of sleep problems, especially in those with hyperactive-impulsive symptoms, may help ameliorate ADHD symptomatology."

"Attention deficit/hyperactivity disorder (ADHD), a common behavioural disorder in children, may be associated with comorbid physical and sleep complaints. Dietary intervention studies have shown convincing evidence of efficacy in reducing ADHD symptoms in children. In this pilot study, we investigated the effects of an elimination diet on physical and sleep complaints in children with ADHD. A group of 27 children . . . were assigned randomly to either a diet group (15/27) or a control group (12/27).

The diet group followed a 5-week elimination diet; the control group adhered to their normal diet. Parents of both groups had to keep an extended diary and had to monitor the behaviour and the physical and sleep complaints of their child conscientiously. . . The number of physical and sleep complaints was significantly decreased in the diet group compared to the control group . . . Specific complaints that were significantly reduced were in three domains: headaches or bellyaches, unusual thirst or unusual perspiration, and sleep complaints. . . An elimination diet may be an effective instrument to reduce physical complaints in children with ADHD, but more research is needed to determine the effects of food on (functional) somatic symptoms in children with and without ADHD."

150 of 200 children [75%] improved on an open trial of a diet free of synthetic food coloring, and 63% of them responded to a single-item challenge of tartrazine. In the double-blind portion, the study identified 24 children as clear reactors, including 19 of the 23 "suspected reactors" [82.5%] . "They were irritable and restless and had sleep disturbance. Significant reactions were observed at all six dose levels. A dose response effect was obtained."

Thirty-one children with behavioural problems and learning difficulties were allergy tested ... 15 of these were given the Australian Version
of the Feingold K.P. diet. Ninety-three per cent responded with improved behaviour in the areas of overactivity,
distractability, impulsiveness and excitability. Sleep and enuresis problems were resolved partially or completely. This
study demonstrates that the aforementioned elimination diet significantly affects behaviour.

Note: Many people who don't "test positive" on such tests still respond well to the diet. Allergy testing may be useful if positive, but does not rule out response to diet management if negative.